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IAEA Types of Radioactive Equilibrium SecularHalf-life of parent much greater (> 100 times) than that of decay product 4

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IAEA Types of Radioactive Equilibrium Half-life of parent only (only 10 times greater) than that of decay product TransientHalf-life of parent only greater (only 10 times greater) than that of decay product 5

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IAEA Differential Equation for Radioactive Series Decay = Sr N Sr - Y N Y dN Y dt Parent and Single Decay Product The instantaneous rate of change of Y-90 is made up of two terms: the production rate, which is equal to the Sr-90 decay rate; and the rate of loss, which is the decay rate of Y-90.

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IAEA Secular Equilibrium Sr N Sr = Y N Y A Sr = A Y At secular equilibrium the activities of the parent and decay product are equal and constant with time 11

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IAEA Decay of 226 Ra to 222 Rn Secular Equilibrium A Rn (t) = A o (1 - e - t ) Rn Ra Beginning with zero activity, the activity of the decay product becomes equal to the activity of the parent within 7 or so half-lives of the decay product 12

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IAEA Example of Transient Equilibrium 132 Te Decays to 132 I Transient Equilibrium Note that: I-132 reaches a maximum activity, after which it appears to decay with the half-life of the parent Te-132. the activity of the decay product can never be higher than the initial activity of its parent. Te-132 - 78.2 hr half life I 132 - 2.2 hr half life 20

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IAEA The principle of transient equilibrium is illustrated by the Molybdenum-Technetium radioisotope generator used in nuclear medicine applications. Given initially that the generator contains 100 mCi of 99 Mo (half-life 66 hours) and no 99m Tc (half-life 6 hours) calculate the: a. time required for 99m Tc to reach its maximum activity b. activity of 99 Mo at this time, and c. activity of 99m Tc at this time Sample Problem